Consider a regular octagon.  How many triangles can be formed whose vertices are the vertices of the octagon?
Solution: No three vertices are collinear, so any combination of 3 vertices will make a triangle. There are 8 ways to choose the first point, 7 ways to choose the second point, and 6 ways to choose the third point, but we must divide by $3!$ since order doesn't matter.  So the answer is $\dfrac{8 \times 7 \times 6}{3!} = \boxed{56}$.